Using Portfolio Returns to Estimate the Probability of Large Jumps

Abstract

Sudden jumps in the stock market have a significant impact on consumers’ wealth. A market crash, in particular, can devastate lives and destabilize the entire economy. Therefore, it would be desirable if consumers, policy makers, and financial intermediaries could better anticipate such events. Unfortunately, it is difficult to infer market crashes, in part because they occur so infrequently. This paper proposes the use of portfolio returns as an additional tool for gauging the probability of market jumps. Sophisticated investors (such as hedge funds) incorporate the probability of such jumps in their asset allocation. Thus, the returns of optimally performing portfolios include this forward-looking information in a way that market returns do not. Portfolio returns allow the econometrician to infer the probability of jumps faster and more accurately than using market returns alone. Indeed, I find that, using portfolio returns, the asymptotic variance of jump estimators can converge to zero.

Keywords: portfolio theory; Merton's problem; jumps; maximum likelihood

JEL Classification: G11, G17